Effective Photon-Photon Interactions in Largely Detuned Optomechanics

We propose to realize effective beam-splitter-like and two-mode-squeezing photon-photon interactions in a strong coupling optomechanical interface by exploiting detuned driving lasers. In this interface, the transitions between the optical system and the mechanical oscillator are suppressed by the large energy offsets, therefore protecting the photon-photon interactions from mechanical dissipations. Moreover, the destructive quantum interference between the eigenmodes of the interface is capable of further reducing the effects of initial mechanical thermal occupations. The interface can serve as a universal block for photon state engineering and hybrid quantum networks in high-temperature thermal bath and without the requirement of cooling the mechanical oscillator to the ground state.